Archive for October, 2011

Part I of this essay provided background information that demonstrates the difficulty of the problem of mental extraction of 13th roots and the efforts of calculators to master it. But can it be possible for us to extract 13th roots of 100-digit numbers without devoting portions of our life to it? With a basic talent in mental arithmetic and some study, it can certainly be done, even if not in record time. We present a new method that involves no logarithms, no antilogarithms and no factoring, one that works with 13th powers that end in 1, 3, 7 or 9 (the cases attempted by record holders). The memorization consists of one table and a few formulas. As always, a printer-friendly PDF version of Parts I and II is linked at the end of this essay.

Mental calculators of note (so-called “lightning calculators”) developed areas of expertise in performing calculations that seem astonishing, even unbelievable, to the rest of us. One such specialty is calculating the 8-digit root of a 13th power of 100 digits. Achieving record times historically required massive memorization and calculating speed, racing through a procedure that remains a mystery to most people. Part I of this essay provides a historical overview of the extraction of 13th roots, including the methods used by a few mental calculators, methods that largely rely on a mix of intensive mental calculation and large-scale rote memorization. It demonstrates the creativity and drive of these marvelous people.

In Part II of this essay we will propose a new method for 13th roots like those posed to lightning calculators that is relatively easy to learn, one that makes this feat feasible for those of us with basic mental math capabilities and a desire to do something amazing. As always, a printer-friendly PDF version of Parts I and II is linked at the end of this essay.

"Civilisation loses its treasures by an unconscious process. It has lost them before it has appreciated that they were in the way of being lost; and when I say 'its treasures' I mean the special discoveries and crafts of mankind."

Hilaire Belloc (1940)

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This journal attempts to capture in brief essays my encounters with the technically elegant but nearly forgotten in the mathematical sciences--artistically creative works that can take our breath away with their brilliance. Please click on the About link above for more details.

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